De-Broglie hypothesized that material particles have wave like properties. Figure shows a small particle in a box. The particle simply bounces back and forth at constant speed. As particles also have wave like properties it can be considered to be a wave reflecting back and forth from the ends of the box. The reflections will create a standing wave analogous to standing wave on a string tied at both ends. Since a standing wave confined to a region can have only selected wavelength, momentum of the particle is quantized. We can safely assume that such a particle only has kinetic energy. This energy must also be quantized.

Bohr model is applied to signly ionized helium `He^(+)` Consider the lines that lie in the visible region of the spectrum. Which of the following transitions can given a photon of visible light?

Options

A. `n=5` to `n=4`
B. `n=7` to `n=4`
C. `n=4` to `n=3`
D. `n=8` to `n=3`

Answer

B

Explanation

`1/lambda=RZ^(2)(1/n^(2)-1/m^(2))`
for H visible is form `2rightarrow3,4,5,6`……….
here`z=2`
`Rightarrow 1/lambda=R(Z^(2)/n^(2)-Z^(2)/m^(2))=R(4/4^(2)-4/m^(2))4/m^(2)=1/6^(2)`
`m=6 to 4,7 to 4`,…….